Any tips or methods to make sure the center of the cake bake evenly? Should I bake at a lower temperature? TIA

I assume it's an ovenproof glass bowl...

Generally, I lower the temperature to 325 and allow it to bake until a toothpick in the dead center comes out clean.

I have baked in a glass pyrex bowl. I put a flower nail in the bottom of the bowl, and baked at 325degrees. It came out great!

Actually it is a stainless steel bowl. Sorry I should have been more specific. Are there any stainless steel bowls that wouldn't be safe to bake with?

yes I have baked in both ...also in odd shaped tin cookie boxes and roasting pans...lined with foil...worked great!! for the larger pans I did use several nails( acutally stainless steel fondue forks) since the flower nails were too short...

I bake all the time in Stainless steel bowl especaily the rond salade bowls from Ikea for when I need to make a round or ball cakes, and they work just like a normal cake pan, just grease them in the same way you would a normal cake pan and I also keep the same temp for the oven, just keep an eye on it when the time gets near to the end HTH

I've used one of my stainless steel bowls before. Just greased/floured bowl,
\\added the batter, then baked at 325º. Comes out great, no nails.